{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Designing Adaptive Experiments to Study Working Memory\n",
    "\n",
    "In most of machine learning, we begin with data and go on to learn a model. In other contexts, we also have a hand in the data generation process. This gives us an exciting opportunity: we can try to obtain data that will help our model learn more effectively. This procedure is called *optimal experimental design* (OED) and Pyro supports choosing optimal designs through the `pyro.contrib.oed` module.\n",
    "\n",
    "When using OED, the data generation and modelling works as follows:\n",
    "\n",
    "1. Write down a Bayesian model involving a design parameter, an unknown latent variable and an observable.\n",
    "1. Choose the optimal design (more details on this later).\n",
    "1. Collect the data and fit the model, e.g. using `SVI`.\n",
    "\n",
    "We can also run multiple 'rounds' or iterations of experiments. When doing this, we take the learned model from step 3 and use it as our prior in step 1 for the next round. This approach can be particularly useful because it allows us to design the next experiment based on what has already been learned: the experiments are *adaptive*.\n",
    "\n",
    "In this tutorial, we work through a specific example of this entire OED procedure with multiple rounds. We will show how to design adaptive experiments to learn a participant's working memory capacity. The design we will be adapting is the *length of a sequence of digits that we ask a participant to remember*. Let's dive into the full details.\n",
    "\n",
    "\n",
    "### The experiment set-up\n",
    "Suppose you, the participant, are shown a sequence of digits\n",
    "\n",
    "$$ 1\\ 4\\ 7\\ 0\\ 9 $$\n",
    "\n",
    "which are then hidden. You have to to reproduce the sequence exactly from memory. In the next round, the length of the sequence may be different\n",
    "\n",
    "$$ 6\\ 5\\ 0\\ 2\\ 8\\ 0 .$$\n",
    "\n",
    "The longest sequence that you can remember is your working memory capacity. In this tutorial, we build a Bayesian model for working memory, and use it to run an adaptive sequence of experiments that very quickly learn someone's working memory capacity.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A model of working memory\n",
    "Our model for a single round of the digits experiment described above has three components: the length $l$ of the sequence that the participant has to remember, the participant's true working memory capacity $\\theta$, and the outcome of the experiment $y$ which indicates whether they were able to remember the sequence successfully ($y=1$) or not ($y=0$). We choose a prior for working memory capacity based on the (in)famous \"The magical number seven, plus or minus two\" [1].\n",
    "\n",
    "**Note**: $\\theta$ actually represents the point where the participant has a 50/50 chance of remembering the sequence correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "\n",
    "\n",
    "sensitivity = 1.0\n",
    "prior_mean = torch.tensor(7.0)\n",
    "prior_sd = torch.tensor(2.0)\n",
    "\n",
    "\n",
    "def model(l):\n",
    "    # Dimension -1 of `l` represents the number of rounds\n",
    "    # Other dimensions are batch dimensions: we indicate this with a plate_stack\n",
    "    with pyro.plate_stack(\"plate\", l.shape[:-1]):\n",
    "        theta = pyro.sample(\"theta\", dist.Normal(prior_mean, prior_sd))\n",
    "        # Share theta across the number of rounds of the experiment\n",
    "        # This represents repeatedly testing the same participant\n",
    "        theta = theta.unsqueeze(-1)\n",
    "        # This define a *logistic regression* model for y\n",
    "        logit_p = sensitivity * (theta - l)\n",
    "        # The event shape represents responses from the same participant\n",
    "        y = pyro.sample(\"y\", dist.Bernoulli(logits=logit_p).to_event(1))\n",
    "        return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability of successfully remembering the sequence is plotted below, for five random samples of $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "\n",
    "# We sample five times from the prior\n",
    "theta = (prior_mean + prior_sd * torch.randn((5,1)))\n",
    "l = torch.arange(1, 16, dtype=torch.float)\n",
    "# This is the same as using 'logits=' in the prior above\n",
    "prob = torch.sigmoid(sensitivity * (theta - l))\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "for curve in torch.unbind(prob, 0):\n",
    "    plt.plot(l.numpy(), curve.numpy(), marker='o')\n",
    "plt.xlabel(\"Length of sequence $l$\")\n",
    "plt.ylabel(\"Probability of correctly remembering\\na sequence of length $l$\")\n",
    "plt.legend([\"Person {}\".format(i+1) for i in range(5)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference in the model\n",
    "\n",
    "With the model in hand, we quickly demonstrate variational inference in Pyro for this model. We define a Normal guide for variational inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.distributions.constraints import positive\n",
    "\n",
    "def guide(l):\n",
    "    # The guide is initialised at the prior\n",
    "    posterior_mean = pyro.param(\"posterior_mean\", prior_mean.clone())\n",
    "    posterior_sd = pyro.param(\"posterior_sd\", prior_sd.clone(), constraint=positive)\n",
    "    pyro.sample(\"theta\", dist.Normal(posterior_mean, posterior_sd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finally specify the following data: the participant was shown sequences of lengths 5, 7 and 9. They remembered the first two correctly, but not the third one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "l_data = torch.tensor([5., 7., 9.])\n",
    "y_data = torch.tensor([1., 1., 0.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now run SVI on the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Neg ELBO: 1.6167092323303223\n",
      "Neg ELBO: 3.706324815750122\n",
      "Neg ELBO: 0.9958380460739136\n",
      "Neg ELBO: 1.0630500316619873\n",
      "Neg ELBO: 1.1738307476043701\n",
      "Neg ELBO: 1.6654635667800903\n",
      "Neg ELBO: 1.296904444694519\n",
      "Neg ELBO: 1.305729627609253\n",
      "Neg ELBO: 1.2626266479492188\n",
      "Neg ELBO: 1.3095542192459106\n"
     ]
    }
   ],
   "source": [
    "from pyro.infer import SVI, Trace_ELBO\n",
    "from pyro.optim import Adam\n",
    "\n",
    "conditioned_model = pyro.condition(model, {\"y\": y_data})\n",
    "svi = SVI(conditioned_model,\n",
    "          guide,\n",
    "          Adam({\"lr\": .001}),\n",
    "          loss=Trace_ELBO(),\n",
    "          num_samples=100)\n",
    "pyro.clear_param_store()\n",
    "num_iters = 5000\n",
    "for i in range(num_iters):\n",
    "    elbo = svi.step(l_data)\n",
    "    if i % 500 == 0:\n",
    "        print(\"Neg ELBO:\", elbo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prior:     N(7.000, 2.000)\n",
      "Posterior: N(7.749, 1.282)\n"
     ]
    }
   ],
   "source": [
    "print(\"Prior:     N({:.3f}, {:.3f})\".format(prior_mean, prior_sd))\n",
    "print(\"Posterior: N({:.3f}, {:.3f})\".format(pyro.param(\"posterior_mean\"),\n",
    "                                            pyro.param(\"posterior_sd\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Under our posterior, we can see that we have an updated estimate for the participant's working memory capacity, and our uncertainty has now decreased."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian optimal experimental design\n",
    "So far so standard. In the previous example, the lengths `l_data` were not chosen with a great deal of forethought. Fortunately, in a setting like this, it is possible to use a more sophisticated strategy to choose the sequence lengths to make the most of every question we ask."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do this using Bayesian optimal experimental design (BOED). In BOED, we are interested in designing experiments that maximise the information gain, which is defined formally as\n",
    "\n",
    "$$ \\text{IG}(l, y) = KL(p(\\theta|y,l)||p(\\theta)) .$$\n",
    "\n",
    "where $KL$ represents the [Kullback-Leiber divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence).\n",
    "\n",
    "In words, the information gain is the KL divergence from the posterior to the prior. It therefore represents the distance we \"move\" the posterior by running an experiment with length $l$ and getting back the outcome $y$.\n",
    "\n",
    "Unfortunately, we will not know $y$ until we actually run the experiment. Therefore, we choose $l$ on the basis of the *expected* information gain [2]\n",
    "\n",
    "$$\\text{EIG}(l) = \\mathbb{E}_{y\\sim p(y|\\theta,l)} [KL(p(\\theta|y,l)||p(\\theta))]. $$\n",
    "\n",
    "Because it features the posterior density $p(y|\\theta,l)$, the EIG is not immediately tractable. However, we can make use of the following variational estimator for EIG [3]\n",
    "\n",
    "$$\\text{EIG}(l) = \\min_q \\mathbb{E}_{\\theta,y \\sim p(\\theta)p(y|\\theta,l)} \\left[ \\log \\frac{p(y|\\theta,l)}{q(y|l)} \\right].$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal experimental design in Pyro\n",
    "Fortunately, Pyro comes ready with tools to estimate the EIG. All we have to do is define the \"marginal guide\" $q(y|l)$ in the formula above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def marginal_guide(design, observation_labels, target_labels):\n",
    "    # This shape allows us to learn a different parameter for each candidate design l\n",
    "    q_logit = pyro.param(\"q_logit\", torch.zeros(design.shape[-2:]))\n",
    "    pyro.sample(\"y\", dist.Bernoulli(logits=q_logit).to_event(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not a guide for inference, like the guides normally encountered in Pyro and used in `SVI`. Instead, this guide samples *only* the observed sample sites: in this case `\"y\"`. This makes sense because conventional guides approximate the posterior $p(\\theta|y, l)$ whereas our guide approximates the marginal $p(y|l)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyro.contrib.oed.eig import marginal_eig\n",
    "\n",
    "# The shape of `candidate_designs` is (number designs, 1)\n",
    "# This represents a batch of candidate designs, each design is for one round of experiment\n",
    "candidate_designs = torch.arange(1, 15, dtype=torch.float).unsqueeze(-1)\n",
    "pyro.clear_param_store()\n",
    "num_steps, start_lr, end_lr = 1000, 0.1, 0.001\n",
    "optimizer = pyro.optim.ExponentialLR({'optimizer': torch.optim.Adam,\n",
    "                                      'optim_args': {'lr': start_lr},\n",
    "                                      'gamma': (end_lr / start_lr) ** (1 / num_steps)})\n",
    "\n",
    "eig = marginal_eig(model,\n",
    "                   candidate_designs,       # design, or in this case, tensor of possible designs\n",
    "                   \"y\",                     # site label of observations, could be a list\n",
    "                   \"theta\",                 # site label of 'targets' (latent variables), could also be list \n",
    "                   num_samples=100,         # number of samples to draw per step in the expectation\n",
    "                   num_steps=num_steps,     # number of gradient steps\n",
    "                   guide=marginal_guide,    # guide q(y)\n",
    "                   optim=optimizer,         # optimizer with learning rate decay\n",
    "                   final_num_samples=10000  # at the last step, we draw more samples\n",
    "                                            # for a more accurate EIG estimate\n",
    "                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the EIG estimates that we found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "plt.plot(candidate_designs.numpy(), eig.detach().numpy(), marker='o', linewidth=2)\n",
    "plt.xlabel(\"$l$\")\n",
    "plt.ylabel(\"EIG($l$)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal design: 7\n"
     ]
    }
   ],
   "source": [
    "best_l = 1 + torch.argmax(eig)\n",
    "print(\"Optimal design:\", best_l.item())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tells us that the first round should be run with a sequence of length 7. Note that, while we might have been able to guess this optimal design intuitively, this same framework applies equally well to more sophisticated models and experiments where finding the optimal design by intuition is more challenging."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a side-effect of training, our marginal guide $q(y|l)$ has approximately learned the marginal distribution $p(y|l)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   l | q(y = 1 | l)\n",
      "   1 | 0.9849993586540222\n",
      "   2 | 0.9676634669303894\n",
      "   3 | 0.9329487681388855\n",
      "   4 | 0.871809720993042\n",
      "   5 | 0.7761920690536499\n",
      "   6 | 0.6436398029327393\n",
      "   7 | 0.4999988079071045\n",
      "   8 | 0.34875917434692383\n",
      "   9 | 0.22899287939071655\n",
      "  10 | 0.13036076724529266\n",
      "  11 | 0.06722454726696014\n",
      "  12 | 0.03191758319735527\n",
      "  13 | 0.015132307074964046\n",
      "  14 | 0.00795808993279934\n"
     ]
    }
   ],
   "source": [
    "q_prob = torch.sigmoid(pyro.param(\"q_logit\"))\n",
    "print(\"   l | q(y = 1 | l)\")\n",
    "for (l, q) in zip(candidate_designs, q_prob):\n",
    "    print(\"{:>4} | {}\".format(int(l.item()), q.item()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elements of this fitted tensor represent the marginal over $y$, for each possible sequence length $l$ in `candidate_designs`. We have marginalised out the unknown $\\theta$ so this fitted tensor shows the probabilities for an 'average' participant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The adaptive experiment\n",
    "\n",
    "We now have the ingredients to build an adaptive experiment to study working memory. We repeat the following steps:\n",
    "\n",
    "1. Use the EIG to find the optimal sequence length $l$\n",
    "2. Run the test using a sequence of length $l$\n",
    "3. Update the posterior distribution with the new data\n",
    "\n",
    "\n",
    "At the first iteration, step 1 is done using the prior as above. However, for subsequent iterations, we use the posterior given all the data so far."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, the \"experiment\" is performed using the following synthesiser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def synthetic_person(l):\n",
    "    # The synthetic person can remember any sequence shorter than 6\n",
    "    # They cannot remember any sequence of length 6 or above\n",
    "    # (There is no randomness in their responses)\n",
    "    y = (l < 6.).float()\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code allows us to update the model as we gather more data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_model(mean, sd):\n",
    "    def model(l):\n",
    "        # Dimension -1 of `l` represents the number of rounds\n",
    "        # Other dimensions are batch dimensions: we indicate this with a plate_stack\n",
    "        with pyro.plate_stack(\"plate\", l.shape[:-1]):\n",
    "            theta = pyro.sample(\"theta\", dist.Normal(mean, sd))\n",
    "            # Share theta across the number of rounds of the experiment\n",
    "            # This represents repeatedly testing the same participant\n",
    "            theta = theta.unsqueeze(-1)\n",
    "            # This define a *logistic regression* model for y\n",
    "            logit_p = sensitivity * (theta - l)\n",
    "            # The event shape represents responses from the same participant\n",
    "            y = pyro.sample(\"y\", dist.Bernoulli(logits=logit_p).to_event(1))\n",
    "            return y\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have everything to run a 10-step experiment using adaptive designs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round 1\n",
      "Asking the participant to remember a sequence of length 7\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 5.788 ± 1.636\n",
      "\n",
      "Round 2\n",
      "Asking the participant to remember a sequence of length 6\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 4.943 ± 1.252\n",
      "\n",
      "Round 3\n",
      "Asking the participant to remember a sequence of length 5\n",
      "Participant remembered correctly\n",
      "Estimate of θ: 5.731 ± 1.043\n",
      "\n",
      "Round 4\n",
      "Asking the participant to remember a sequence of length 6\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 5.261 ± 0.928\n",
      "\n",
      "Round 5\n",
      "Asking the participant to remember a sequence of length 5\n",
      "Participant remembered correctly\n",
      "Estimate of θ: 5.615 ± 0.859\n",
      "\n",
      "Round 6\n",
      "Asking the participant to remember a sequence of length 6\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 5.423 ± 0.888\n",
      "\n",
      "Round 7\n",
      "Asking the participant to remember a sequence of length 6\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 5.092 ± 0.763\n",
      "\n",
      "Round 8\n",
      "Asking the participant to remember a sequence of length 5\n",
      "Participant remembered correctly\n",
      "Estimate of θ: 5.371 ± 0.717\n",
      "\n",
      "Round 9\n",
      "Asking the participant to remember a sequence of length 5\n",
      "Participant remembered correctly\n",
      "Estimate of θ: 5.597 ± 0.720\n",
      "\n",
      "Round 10\n",
      "Asking the participant to remember a sequence of length 6\n",
      "Participant could not remember the sequence\n",
      "Estimate of θ: 5.434 ± 0.640\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ys = torch.tensor([])\n",
    "ls = torch.tensor([])\n",
    "history = [(prior_mean, prior_sd)]\n",
    "pyro.clear_param_store()\n",
    "current_model = make_model(prior_mean, prior_sd)\n",
    "\n",
    "for experiment in range(10):\n",
    "    print(\"Round\", experiment + 1)\n",
    "     \n",
    "    # Step 1: compute the optimal length\n",
    "    optimizer = pyro.optim.ExponentialLR({'optimizer': torch.optim.Adam,\n",
    "                                          'optim_args': {'lr': start_lr},\n",
    "                                          'gamma': (end_lr / start_lr) ** (1 / num_steps)})\n",
    "    eig = marginal_eig(current_model, candidate_designs, \"y\", \"theta\", num_samples=100,\n",
    "                       num_steps=num_steps, guide=marginal_guide, optim=optimizer,\n",
    "                       final_num_samples=10000)\n",
    "    best_l = 1 + torch.argmax(eig).float().detach()\n",
    "    \n",
    "    # Step 2: run the experiment, here using the synthetic person\n",
    "    print(\"Asking the participant to remember a sequence of length\", int(best_l.item()))\n",
    "    y = synthetic_person(best_l)\n",
    "    if y:\n",
    "        print(\"Participant remembered correctly\")\n",
    "    else:\n",
    "        print(\"Participant could not remember the sequence\")\n",
    "    # Store the sequence length and outcome\n",
    "    ls = torch.cat([ls, best_l.expand(1)], dim=0)\n",
    "    ys = torch.cat([ys, y.expand(1)])\n",
    "    \n",
    "    # Step 3: learn the posterior using all data seen so far\n",
    "    conditioned_model = pyro.condition(model, {\"y\": ys})\n",
    "    svi = SVI(conditioned_model,\n",
    "              guide,\n",
    "              Adam({\"lr\": .005}),\n",
    "              loss=Trace_ELBO(),\n",
    "              num_samples=100)\n",
    "    num_iters = 2000\n",
    "    for i in range(num_iters):\n",
    "        elbo = svi.step(ls)\n",
    "        \n",
    "    history.append((pyro.param(\"posterior_mean\").detach().clone().numpy(),\n",
    "                    pyro.param(\"posterior_sd\").detach().clone().numpy()))\n",
    "    current_model = make_model(pyro.param(\"posterior_mean\").detach().clone(),\n",
    "                               pyro.param(\"posterior_sd\").detach().clone())\n",
    "    print(\"Estimate of \\u03b8: {:.3f} \\u00b1 {:.3f}\\n\".format(*history[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's visualize the evolution of the posterior over $\\theta$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.colors as colors\n",
    "import matplotlib.cm as cmx\n",
    "\n",
    "\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "cmap = plt.get_cmap('winter') \n",
    "cNorm  = colors.Normalize(vmin=0, vmax=len(history)-1)\n",
    "scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=cmap)\n",
    "plt.figure(figsize=(12, 6))\n",
    "x = np.linspace(0, 14, 100)\n",
    "for idx, (mean, sd) in enumerate(history):\n",
    "    color = scalarMap.to_rgba(idx)\n",
    "    y = norm.pdf(x, mean, sd)\n",
    "    plt.plot(x, y, color=color)\n",
    "    plt.xlabel(\"$\\\\theta$\")\n",
    "    plt.ylabel(\"p.d.f.\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Blue = prior, light green = 10 step posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By contrast, suppose we use a simplistic design: try sequences of lengths 1, 2, ..., 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "pyro.clear_param_store()\n",
    "ls = torch.arange(1, 11, dtype=torch.float)\n",
    "ys = synthetic_person(ls)\n",
    "conditioned_model = pyro.condition(model, {\"y\": ys})\n",
    "svi = SVI(conditioned_model,\n",
    "          guide,\n",
    "          Adam({\"lr\": .005}),\n",
    "          loss=Trace_ELBO(),\n",
    "          num_samples=100)\n",
    "num_iters = 2000\n",
    "for i in range(num_iters):\n",
    "    elbo = svi.step(ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "y1 = norm.pdf(x, pyro.param(\"posterior_mean\").detach().numpy(),\n",
    "              pyro.param(\"posterior_sd\").detach().numpy())\n",
    "y2 = norm.pdf(x, history[-1][0], history[-1][1])\n",
    "plt.plot(x, y1)\n",
    "plt.plot(x, y2)\n",
    "plt.legend([\"Simple design\", \"Optimal design\"])\n",
    "plt.xlabel(\"$\\\\theta$\")\n",
    "plt.ylabel(\"p.d.f.\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although both design strategies give us data, the optimal strategy ends up with a posterior distribution that is more peaked: that means we have greater confidence in our final answer, or may be able to stop experimenting earlier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extensions\n",
    "\n",
    "In this tutorial we used variational inference to fit an approximate posterior for $\\theta$. This could be substituted for an alternative posterior inference strategy, such as Hamiltonian Monte Carlo. \n",
    "\n",
    "The model in this tutorial is very simple and could be extended in a number of ways. For instance, it's possible that as well as measuring whether the participant did or did not remember the sequence, we might collect some other information as well. We could build a model for the number of mistakes made (e.g. the edit distance between the correct sequence and the participant's response) or jointly model the correctness and the time taken to respond. Here is an example model where we model the response time using a LogNormal distribution, as suggested by [4]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_intercept = 0.5\n",
    "time_scale = 0.5\n",
    "\n",
    "def model(l):\n",
    "    theta = pyro.sample(\"theta\", dist.Normal(prior_mean, prior_sd))\n",
    "    logit_p = sensitivity * (theta - l)\n",
    "    correct = pyro.sample(\"correct\", dist.Bernoulli(logits=logit_p))\n",
    "    mean_log_time = time_intercept + time_scale * (theta - l)\n",
    "    time = pyro.sample(\"time\", dist.LogNormal(mean_log_time, 1.0))\n",
    "    return correct, time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It would still be possible to compute the EIG using `marginal_eig`. We would replace `\"y\"` by `[\"correct\", \"time\"]` and the marginal guide would now model a joint distribution over the two sites `\"correct\"` and `\"time\"`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model also made a number of assumptions that we may choose to relax. For instance, we assumed that all sequences of the same length are equally easy to remember. We also fixed the `sensitivity` to be a known constant: it's likely we would need to learn this. We could also think about learning at two levels: learning global variables for population trends as well as local variables for individual level effects. The current model is an individual only model. The EIG could still be used as a means to select the optimal design in such scenarios."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Miller, G.A., 1956. **The magical number seven, plus or minus two: Some limits on our capacity for processing information.** Psychological review, 63(2), p.81.\n",
    "\n",
    "[2] Chaloner, K. and Verdinelli, I., 1995. **Bayesian experimental design: A review.** Statistical Science, pp.273-304.\n",
    "\n",
    "[3] Foster, A., Jankowiak, M., Bingham, E., Horsfall, P., Teh, Y.W., Rainforth, T. and Goodman, N., 2019. **Variational Bayesian Optimal Experimental Design.** Advances in Neural Information Processing Systems 2019 (to appear).\n",
    "\n",
    "[4] van der Linden, W.J., 2006. **A lognormal model for response times on test items.** Journal of Educational and Behavioral Statistics, 31(2), pp.181-204."
   ]
  }
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